Triple-Point Wetting on Rough Substrates

Abstract

The influence of substrate roughness on the wetting scenario of adsorbed van der Waals films is investigated by theory and experiment. Calculating the bending free energy penalty of a solid sheet picking up the substrate roughness, we show that a finite roughness always leads to triple-point wetting reducing the widths of the adsorbed solid films considerably as compared to that of smooth substrates. Testing the theory against our experimental data for molecular hydrogen adsorbed on gold, we find quantitative agreement. DOI: 10.1103/PhysRevLett.88.055702 PACS numbers: 64.70.Hz, 67.70. +n, 68.08.Bc, 68.35.Rh Wetting of a solid substrate, exposed to a gas in thermodynamic equilibrium, is an ubiquitous phenomenon, with both fundamental aspects [1,2] and important applications [3 -5]. Microscopically, substrate wetting by a liquid film is caused by a strong substrate-particle attraction mediated by van der Waals forces. At present, an almost complete microscopic understanding of wetting on flat solid substrates is available [1,2,6] predicting the thickness of the liquid film as a function of the substrate-particle and interparticle interactions for given thermodynamic parameters such as temperature and pressure. The following basic theoretical predictions were confirmed by experiments using, e.g., noble gases [1] on different substrates: (i) For fixed thermodynamic conditions, the thickness of the wetting layer grows for increasing substrate-particle attraction. (ii) Complete wetting (i.e., a diverging thickness of the liquid layer) occurs if the substrate-particle attraction is stronger than the interparticle interaction and the thermodynamic conditions approach liquid-gas coexistence. The latter condition can be achieved only if the system temperature T is above the triple temperature T 3 . For T , T 3 , on the other hand, a solid film shows up near the sublimation line. Various experiments have shown [7][8][9][10] that the width of the solid layer always remains finite when approaching gas-solid coexistence. It is only near the triple point that a liquid layer on top of the solid sheet is formed, with a diverging width as the triple point is approached. This universal behavior is called "triple-point wetting."One major difference between a liquid and solid wetting layer is that a solid cannot relax the elastic compression caused by the substrate attraction as embodied in the (reduced) wall-particle Hamaker constant R. This fact is the basic ingredient in the traditional Gittes-Schick theory [11] of solid adsorption on flat substrates. It predicts that, for a particular value R R 0 of the substrate attraction, complete wetting is possible, while for R . R 0 , in contrast to liquid wetting, the thickness of the solid film ᐉ s decreases with increasing R. In this Letter we show that the key parameter governing adsorption of solid films is the substrate roughness rather than the elastic deformation caused by the substrate attraction. As a result of our theoretical analysis, a finite substrate roughness leads inev...

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